CRM CAMP in Nonlinear Analysis

Preuves mathématiques assistées par ordinateur en analyse non linéaire

10 novembre 2020 de 10 h 00 à 11 h 00 (heure de Montréal/HNE) Réunion Zoom

Recent progress in proving stability of traveling waves in the 1D Navier-Stokes equations using rigorous computations

Séminaire par Blake Barker (Brigham Young University, USA)

We discuss recent progress developing and applying rigorous computation to prove stability of traveling waves in the 1D Navier-Stokes equation. In particular, we talk about rigorous computation of the Evans function, an analytic function whose zeros correspond to eigenvalues of the linearized PDE problem. Nonlinear stability results by Zumbrun and collaborators show that the underlying traveling waves are stable if there are no eigenvalues in the right half of the complex plane. Thus one may use rigorous computation of the Evans function to prove nonlinear-orbital stability of traveling waves.